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According to the topology design theory and method of parallel mechanism (PM) based on position and orientation characteristic (POC) equations, a new type of three translation (3T) PM with symbolic positive position solutions and partial motion decoupling was designed. Firstly, its topological characteristics were analyzed, and the values of its main topological features, such as POC, DOF and κ, were obtained. Secondly, the symbolic positive position solutions of the PM were obtained according to the positive kinematics modeling principle based on topological characteristics proposed by the authors. The correctness of the positive position solution was verified by the numerical model. The inverse position solution was solved and verified, The workspace of the PM was solved based on the inverse solution formula. Furthermore, the screw theory was used to solve the transmission wrench screw and the output twist screw of each branch chain. The kinematic/force transmission performance index of the mechanism were solved. The curves of input transmission index (LTI), output transmission index (OTI) and local transmission index were drawn by Matlab, According to the expression of the reciprocal product of the input twist screw and the transmission wrench screw, the expression of the output twist screw and the transmission wrench screw, and linearly independent numbers of three constraint wrench screw, the singular configuration of the mechanism was analyzed. Finally, according to the curve of LTI, the distance between each point in the workspace and the singular configuration was evaluated.